Imaging optical system and image reading apparatus using the same

ABSTRACT

Obtained are an imaging optical system having a simple structure in which imaging position deviation due to deformation caused by a weight of an off-axial optical element is reduced and an image reading apparatus using the same. According to an imaging optical system for image reading, image information on an original surface is imaged on a sensor, and is read by the sensor. The imaging optical system includes reflection-type off-axial optical elements, each of which has an outer shape whose lengths in directions orthogonal to each other are different from each other and whose thickness is smaller than a length of the outer shape in a short-direction thereof and is made of a resin material. The plurality of off-axial optical elements are disposed such that mirror surfaces thereof are opposed to each other and constructed to satisfy a conditional expression.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an imaging optical system and an imagereading apparatus using the imaging optical system. In particular, thepresent invention is suitable for reading a monochrome image or a colorimage using a line sensor of an image scanner, a digital copyingmachine, or the like in which various aberrations are corrected in abalanced manner to perform image reading with high resolution.

2. Related Background Art

Up to now, various image reading apparatuses have been proposed to readimage information on a surface of an original. According to the proposedimage reading apparatuses, a line sensor in which a plurality of lightreceiving elements are arranged in a main scanning direction is used toimage the image information on a surface of the line sensor (CCD). Theoriginal and the line sensor are moved relative to each other in asub-scanning direction to read the image information on the surface ofthe original or the like based on output signals obtained by the linesensor.

FIG. 7 is a schematic view showing a conventional image readingapparatus of a carriage integral type scanning system. In FIG. 7, anoriginal 87 placed on an original table glass 82 is directly illuminatedwith a light beam emitted from an illumination light source 81. A lightbeam reflected on the original 87 travels through a first return mirror83 a, a second return mirror 83 b, and a third return mirror 83 c inthis order, the light beam having its optical path bent in an innerportion of a carriage 86. Then, the light beam is imaged on a surface ofa line sensor 85 by an imaging lens (imaging optical system) 84.

After that, the carriage 86 is moved in a direction indicated by anarrow A (sub-scanning direction) shown in FIG. 7 by a sub-scanning motor88 to read the image information on the original 87. The line sensor 85shown in FIG. 7 is composed of a plurality of light receiving elementsarranged in a one-dimensional direction (main scanning direction).

FIG. 8 is an explanatory view showing a fundamental structure of areading optical system of the image reading optical system shown in FIG.7.

In FIG. 8, the reading optical system includes the imaging opticalsystem 84 and the line sensor 85. The line sensor 85 is composed of linesensors 85R, 85G, and 85B for reading color information of R (red), G(green), and B (blue). Reading areas 87R, 87G, and 87B are set on thesurface of the original 87 corresponding to the line sensors 85R, 85G,and 85B.

When the surface of the original 87 is scanned, the same location can beread in different colors at a certain time interval. In the case wherethe imaging optical system 84 includes an ordinary refracting system inthe above-mentioned structure, longitudinal chromatic aberration andlateral chromatic aberration occur. Therefore, defocus or positionalmisregistration occurs in line images to be formed on the line sensors85B and 85R as compared with the case of the line sensor 85G serving asa reference sensor. Thus, when the respective color images aresuperimposed for reproduction, color bleeding or misregistration isconspicuous in a resultant image. That is, when high-apertureperformance and high-resolution performance are required, suchrequirements cannot be satisfied.

On the other hand, according to recent proposals, even in the case of anon-coaxial optical system, it is possible to construct an opticalsystem whose aberrations are sufficiently corrected by introducing theconcept of a reference axis to make constituent surfaces thereofasymmetrical and aspherical (see Japanese Patent Application Laid-OpenNo. H09-005650, Japanese Patent Application Laid-Open No. H08-292371,and Japanese Patent Application Laid-Open No. H08-292372). An example ofa designing method of the optical system is disclosed in Japanese PatentApplication Laid-Open H09-005650 and design examples thereof aredisclosed in Japanese Patent Application Laid-Open H08-292371 andJapanese Patent Application Laid-Open No. H08-292372.

Such a non-coaxial optical system is called an off-axial optical system.The off-axial optical system is defined as an optical system including acurved surface (an off-axial curved surface) in which, when a referenceaxis is set along a light beam passing through the center of an imageand the center of a pupil, a surface normal to a constituent surface atan intersection with the reference axis is not on the reference axis. Atthis time, the reference axis becomes a bent shape.

In the off-axial optical system, a constituent surface thereof normallybecomes non-coaxial and no eclipse occurs even on a reflective surfacethereof, so an optical system using the reflective surface is easy toconstruct. The off-axial optical system also has advantages that anoptical path can be relatively freely drawn and that an integral typeoptical system is easy to produce by using a method of integrallymolding constituent surfaces.

There has been disclosed an imaging optical system for image reading towhich such a technique is adopted (see Japanese Patent ApplicationLaid-Open No. 2002-335375) When the disclosed technique is used, anoff-axial optical system including five or six reflective surfaces(off-axial reflective surfaces) in which there is no chromaticaberration and other aberrations are sufficiently corrected is achievedin an image reading apparatus. In addition to this, the image formingoptical apparatus is reduced in size, so an optical system suitable fora carriage integral type is provided in the example.

It has been disclosed an imaging optical system for image reading towhich the same technique is adopted (see Japanese Patent ApplicationLaid-Open No. 2003-057549) In the example, an off-axial optical systemincluding three reflective surfaces (off-axial reflective surfaces) isdisclosed, which has an optical path length sufficient for anapplication to a 2:1 mirror scanning type scanner.

There has been disclosed an invention as to positional deviation of animaging plane resulting from a change in temperature occurring in thecase where a resin material is used to simplify the off-axial opticalsystem (to reduce a cost) (see Japanese Patent Application Laid-Open No.2003-287683).

On the other hand, in the case of such a reflection type off-axialoptical system, it is difficult to maintain preferable opticalperformances with each of surfaces thereof formed in a spherical shape.However, when at least one surface is formed to be an aspherical surface(free surface) which is rotational asymmetrical, the preferable opticalperformances can be achieved.

It has been generally known that an optical system composed ofrefractive surfaces is sensitive to decentering. When a reflection typeoptical element having the aspherical surface (free surface) which isrotational asymmetrical is to be incorporated in the off-axial opticalsystem, it is required that, in addition to the precision of a normalspherical reflective surface, a member for holding the normal sphericalreflective surface and the reflection type optical element be formedwith high precision.

In the case where the off-axial optical reflective surface is areflective surface having a free surface shape, production of theoff-axial optical system made of normal glass makes its manufacturingprocess complicated, which increases a cost thereof. In order to dealwith such a problem, for example, the off-axial optical system may bemade of plastic such as polycarbonate, acrylic, or polyolefin. However,in addition to a problem with the misregistration of an imaging positionresulting from a change of environment, particularly, a change intemperature as described in Japanese Patent Application Laid-Open No.2003-287683, there occurs another problem in that the optical element(off-axial optical element) deforms under its own weight to deviate theimaging position.

A resin material, which is normally used as an optical material, has aflexural modulus much smaller than that of a glass material, so theresin material easily deforms. When strength is merely provided to anoptical element so as to prevent the optical element from deformingunder its own weight, the optical element is made large and thickened.Thus, a time for molding the optical element lengthens or the number ofcavities reduces, which leads to a problem in that manufacturing becomesdifficult (thereby increasing a cost).

SUMMARY OF THE INVENTION

An object of the present invention is to provide an imaging opticalsystem having a simple structure in which deviation of an imagingposition due to deformation caused by a weight of an off-axial opticalelement is reduced and an image reading apparatus using the imagingoptical system. In particular, an object of the present invention is toprovide an image reading apparatus suitable for the case where a resinmaterial is used as a material of the off-axial optical element.

According to one aspect of the invention, an imaging optical system forimage reading, in which image information on a surface of an original isimaged on a line sensor and the image information is read by the linesensor, includes:

a plurality of off-axial optical elements, each of which is a reflectiontype and made of a resin material,

and in the imaging optical system for image reading, when a linedirection of the line sensor is a main scanning direction and adirection orthogonal to the main scanning direction is a sub-scanningdirection,

a length of each of the off-axial optical elements in the main scanningdirection is longer than a length thereof in the sub-scanning directionand a thickness of each of the off-axial optical elements is smallerthan the length thereof in the sub-scanning direction,

and also in the imaging optical system for image reading, in asub-scanning section in which the main scanning direction corresponds toa normal, the following condition is satisfied,−30°<θa−θb<30°,where θa represents an absolute value of a first angle formed between asurface normal to a reflective surface of a first off-axial opticalelement of the plurality of off-axial optical elements at a reflectionpoint of the reflective surface of the first off-axial optical elementon which a reference axis light beam is reflected and an optical path ofa reference axis light beam incident on the imaging optical system andθb represents an absolute value of a second angle formed between asurface normal to a reflective surface of a second off-axial opticalelement opposed to the reflective surface of the first off-axial opticalelement at a reflection point of the reflective surface of the secondoff-axial optical element on which the reference axis light beam isreflected and the optical path of the reference axis light beam incidenton the imaging optical system.

According to a further aspect of the invention, in the imaging opticalsystem for image reading, each of the off-axial optical elementscomprises a reflective surface which is symmetrical with respect to areference axis in the main scanning direction and asymmetrical withrespect to the reference axis in the sub-scanning direction.

According to a further aspect of the invention, in the imaging opticalsystem for image reading, the plurality of off-axial optical elementsinclude thicknesses different from one another.

According to a further aspect of the invention, in the imaging opticalsystem for image reading, when n is a positive integer, the imagingoptical system comprises 2n (0<n<3) off-axial optical elements.

According to a further aspect of the invention, in the imaging opticalsystem for image reading, the plurality of off-axial optical elementsare held in a holding portion of a lens barrel, and the off-axialoptical elements are different from one another in a position of aportion of the off-axial optical element which abuts the holding portionof the lens barrel.

According to a further aspect of the invention, in the imaging opticalsystem for image reading, when a thickness of an arbitrary off-axialoptical element of the plurality of off-axial optical elements isexpressed by Lz and a length thereof in the sub-scanning direction isexpressed by Ly, the Following condition is satisfied,1.5<Ly/Lz<20where Lz represents a thickness of an arbitrary off-axial opticalelement of said plurality of off-axial optical elements and Lyrepresents said length in the sub-scanning direction.

According to a further aspect of the invention, the imaging opticalsystem for image reading further includes an aperture stop located on anoptical path between the first off-axial optical element and the secondoff-axial optical element.

According to another aspect of the invention, an image reading apparatusincludes the imaging optical system for image reading set out in theforegoing; an original table on which the original is placed; and theline sensor.

According to the present invention, it is possible to obtain an imagingoptical system which is used for an image reading apparatus including aline sensor and an imaging optical system composed of an off-axialoptical element made of a resin material, such as an image scanner or adigital copying machine, and which has a simple structure in whichdeviation of an imaging position due to deformation caused by a weightof the off-axial optical element is reduced. In addition, it is possibleto obtain the image reading apparatus using the imaging optical system.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic view showing a principal part of an image readingapparatus according to Embodiment 1 of the present invention;

FIG. 2 is a sectional view showing an imaging optical system accordingto Embodiment 1 of the present invention;

FIG. 3 is a schematic view showing a principal part of an image readingapparatus according to Embodiment 2 of the present invention;

FIG. 4 is a sectional view showing an imaging optical system accordingto Embodiment 2 of the present invention;

FIG. 5 is a schematic view showing a principal part of an image readingapparatus according to Embodiment 3 of the present invention;

FIG. 6 is a sectional view showing an imaging optical system accordingto Embodiment 3 of the present invention;

FIG. 7 is a schematic view showing a principal part of a conventionalimage reading apparatus;

FIG. 8 is a fundamental structural view showing a color image readingapparatus; and

FIG. 9 is a diagram for explaining a definition of an off-axial opticalsystem.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

An indicating manner of constituent specifications of an imaging opticalsystem (optical system) used in each of the embodiments of the presentinvention and common items to all the embodiments will be describedbefore the description of each of the embodiments.

FIG. 9 is an explanatory diagram showing a coordinate system fordefining constituent data of an imaging optical system according to thepresent invention. In each of the embodiments, assume that an i-th planelocated on an optical path of a light beam (reference axis light beamLa1 which is indicated by a dashed line in FIG. 9 and described later)traveling from an object side to an imaging plane is an i-th plane.

In FIG. 9, a first plane R1 indicates an aperture stop. A second planeR2 indicates a refractive surface which is coaxial to the first planeR1. A third plane R3 indicates a reflective surface tilted relative tothe second plane R2. A fourth plane R4 indicates a reflective surfacewhich is shifted and tilted relative to the third plane R3. A fifthplane R5 indicates a reflective surface which is shifted and tiltedrelative to the fourth plane R4. A sixth plane R6 indicates a reflectivesurface which is shifted and tilted relative to the fifth plane R5. Aseventh plane R7 indicates a refractive surface which is shifted andtilted relative to the sixth plane R6. The respective planes of thesecond plane R2 to the seventh plane R7 are provided in an opticalelement made of a transparent medium such as glass or plastic.

Therefore, in the structure shown in FIG. 9, a medium between an objectplane (not shown) and the second plane R2 is air, a medium between thesecond plane R2 and the seventh plane R7 is a common medium, and amedium between the seventh plane R7 and an eighth plane (such as animaging plane) R8 is air.

The imaging optical system according to the present invention is anoff-axial optical system, so the second plane R2 to the seventh plane R7composing the imaging optical system do not include a common opticalaxis.

Therefore, first, an absolute coordinate system in which the center ofan effective light beam diameter of the first plane R1 is an origin isset in each of the embodiments. Then, in each of the embodiments, acenter point of the effective light beam diameter of the first plane R1is set as an origin. An optical path of the light beam (reference axislight beam) La1 passing through the origin and the final imaging planeR8 is defined as a reference axis La of the imaging optical system. Thereference axis La in each of the embodiments has a direction(orientation). The direction corresponds to a direction in which thereference axis light beam La1 travels for imaging.

In each of the embodiments of the present invention, the reference axisof the imaging optical system as a reference is set as described above.The reference axis to be employed for the imaging optical system may bean axis that is appropriate in view of an optical design of the system,attaining correct aberrations in a balanced manner, or expressingrespective plane shapes composing the imaging optical system. However,an optical path of a light beam passing through the center of theimaging plane and any one of an aperture stop, an entrance pupil, anexit pupil, the center of the first plane of the imaging optical system,and the center of the final plane thereof, is normally set as thereference axis of the imaging optical system as a reference.

In other words, the optical path of the light beam (reference axis lightbeam) which passes through the center point of the effective light beamdiameter of the first plane R1, that is, the surface of the aperturestop, is refracted by the refractive surfaces and deflected on thereflective surfaces, and reaches the center of the final imaging planeis set as the reference axis La in each of the embodiments of thepresent invention. The order of each of the surfaces is setcorresponding to an order in which the reference axis light beam La1 issubjected to refraction or reflection.

Thus, the direction of the reference axis La is changed according to theset order of each of the surfaces based on the law of refraction orreflection, and the reference axis La finally reaches the center of theimaging plane.

All tilt surfaces composing the imaging optical system according to eachof the embodiments of the present invention are fundamentally tiltedwithin the same plane. Therefore, each axis of absolute coordinatesystem is determined as follows.

-   Z-axis: Reference axis that passes through the origin and extends to    the second plane R2-   Y-axis: Straight line that passes through the origin and is rotated    counterclockwise by 90° relative to the Z-axis within a tilt plane    (paper of FIG. 9)-   X-axis: Straight line that passes through the origin and is    perpendicular to each of the Z-axis and the Y-axis (straight line    perpendicular to the paper of FIG. 9)

A plane shape of the i-th plane composing the imaging optical system isexpressed by using a local coordinate system, in which an intersectionof the reference axis and the i-th plane is set as an origin, so thatthe plane shape can be recognized more easily, rather than by using theabsolute coordinate system. Therefore, in the embodiment showingconstituent data with respect to the imaging optical system according tothe present invention, the plane shape of the i-th plane is expressed byusing the local coordinate system.

A tilt angle of the i-th plane within the YZ plane is expressed by anangle θi (unit: degree) in a case where a counterclockwise directionrelative to the Z-axis of the absolute coordinate system is positive.Therefore, in each of the embodiments of the present invention, a localcoordinate origin of each plane is located on the YZ plane shown in FIG.9. There is no plane decentering on each of the XZ plane and the XYplane. The y- and z-axes of the local coordinates (x, y, and z) of thei-th plane are tilted relative to the absolute coordinate system (X, Y,Z) within the YZ plane by the angle θi, and more specifically set asfollows.

-   z-axis: Straight line that passes through the origin of the local    coordinate system and is rotated counterclockwise by the angle θi    relative to the Z-direction of the absolute coordinate system within    the YZ-plane-   y-axis: Straight line that passes through the origin of the local    coordinate system and is rotated counterclockwise by 90° relative to    the z-direction within the YZ plane-   x-axis: Straight line that passes through the origin of the local    coordinate system and is perpendicular to the YZ-plane

Reference symbol Di denotes a scalar indicating an interval between theorigins of the local coordinate systems of the i-th plane and an (i+1)thplane. Reference symbols Ndi and vdi denote a refractive index of amedium between the i-th plane and the (i+1)th plane and Abbe numberthereof, respectively.

In each of the embodiment of the present invention, the sectional viewof the optical system and numerical data thereof are provided.

A spherical surface has a shape expressed by the following expression.z=((x ² +y ²)/r _(i))/(1+(1−(x ² +y ²)/r _(i) ²)^(1/2)

The imaging optical system according to each of the embodiments of thepresent invention has an aspherical surface which is rotationalasymmetrical. A shape of the aspherical surface is expressed by thefollowing expression.z=C ₀₂ y ² +C ₂₀ x ² +C ₀₃ y ³ +C ₂₁ x ² y+C ₀₄ y ⁴ +C ₂₂ x ² y ² +C ₄₀x ⁴ +C ₀₅ y ⁵ +C ₂₃ x ² y ³ +C ₄₁ x ⁴ y+C ₀₆ y ⁶ +C ₂₄ x ² y ⁴ +C ₄₂ x ⁴y ² +C ₆₀ x ⁶

The above-mentioned curved surface expression holds only an even numberorder term for x, so a curved surface specified by the curved surfaceexpression has a surface symmetrical shape with respect to the yz-planeas a symmetrical surface.

The imaging optical system according to each of the embodiments is not acoaxial optical system, so it is difficult to directly calculate a focallength based on paraxial theory. Therefore, a conversion focal lengthf_(eq) defined by the following expression is used.f _(eq) =h ₁/tan(a _(k)′)

By definition when the number of reflective surfaces is odd, a sign ofthe focal length is expressed in reverse to a normal sign. Here, h₁represents incident height of a light beam incident on the first planefrom a direction which is parallel to the reference axis and closest tothe reference axis, and a_(k)′ represents angle formed between adirection of the light beam exited from the final plane and thereference axis.

Embodiment 1

FIG. 1 is a schematic sub-scanning sectional view showing a principalpart of an image reading apparatus to which an imaging optical systemaccording to Embodiment 1 of the present invention is applied.

FIG. 2 is a schematic sub-scanning sectional view in a case where theimaging optical system 4 shown in FIG. 1 is extracted.

In FIG. 1, a light source (light source means) 1 is composed of afluorescent lamp, a xenon lamp, or the like. An original (object) 7 isplaced on an original table glass 2. Reference numerals 3 a, 3 b, and 3c indicate a first reflecting mirror, a second reflecting mirror, and athird reflecting mirror, respectively.

A light beam based on image information of an original 7 is imaged on aline sensor 5 serving as a reading means by an imaging optical system(off-axial optical system) 4 for image reading.

In this embodiment, the imaging optical system 4 includes two first andsecond reflection type off-axial optical elements (reflection typeoff-axial optical elements) 4 a and 4 b which are disposed in the statedorder from the original 7 side, each of which has an outer shape inwhich lengths in directions orthogonal to each other are different fromeach other. Each of the first and second off-axial optical elements 4 aand 4 b has a thickness smaller than a short-directional length of theouter shape and is made of a resin material. Mirror surfaces (off-axialreflective surface) R2 and R4 of the first and second off-axial opticalelements 4 a and 4 b are opposed to each other. Each of the first andsecond off-axial optical elements 4 a and 4 b more specifically has arectangular shape and is formed such that a length thereof in athickness direction is shorter than a short-directional (short-sidedirectional) length thereof.

In this embodiment, each of the mirror surfaces (off-axial reflectivesurfaces) of the first and second off-axial optical elements 4 a and 4 bhas a main scanning directional (long-directional) length which islonger than a sub-scanning directional (short-directional) length and amain scanning directional (long-directional) thickness which is smallerthan a sub-scanning directional (short-directional) length.

An aperture stop SP (R3) is disposed between the first off-axial opticalelement 4 aand the second off-axial optical element 4 b.

A line sensor (light receiving means) 5 is composed of a CCD or thelike, and disposed in a position corresponding to the imaging plane. Acarriage (case) 6 houses the light source 1, the first reflecting mirror3 a, the second reflecting mirror 3 b, the third reflecting mirror 3 c,the imaging optical system 4, and the line sensor 5.

Here, a pixel arrangement direction (direction perpendicular to thepaper, an X-direction) of the line sensor 5 corresponds to a mainscanning direction, and a direction orthogonal to the main scanningdirection (direction within the paper, a Y-direction) corresponds to asub-scanning direction. Assume that a traveling direction of a lightbeam is a Z-direction. At this time, an XY plane corresponds to a mainscanning section, and a YZ plane corresponds to a sub-scanning section.

In this embodiment, the original (object) 7 placed on the original tableglass 2 is illuminated with a light beam emitted from the light source1. A light beam reflected on the original 7 travels through the firstreflecting mirror 3 a, the second reflecting mirror 3 b, and the thirdreflecting mirror 3 c. Then, the light beam is imaged on the line sensor5 by the imaging optical system 4. At this time, the original 7 and thecarriage 6 are moved relative to each other in the sub-scanningdirection (direction indicated by an arrow A) to two-dimensionally readthe original 7.

In order to make the image reading apparatus compact, an optical path ofthe light beam is folded using the first reflecting mirror 3 a, thesecond reflecting mirror 3 b, and the third reflecting mirror 3 c. Theimaging optical system 4 also contributes to fold the optical path. Theoptical path is folded in a substantial Z-shape in the imaging opticalsystem 4 to facilitate the canceling of decentering caused in theoff-axial reflective surfaces R2 and R4. Therefore, preferable imagingperformance is obtained regardless of the structure having the surfaceswhich is as small in number as two.

In order to obtain more preferable imaging performance, the off-axialreflective surfaces R2 and R4 are formed in an asymmetrical free surfaceshape with respect to the sub-scanning section (YZ-plane) within thesub-scanning section. Therefore, decentering caused by folding theoptical path in the sub-scanning direction is preferably corrected.

As shown in FIG. 2, an incident reference axis light beam 12 incident onthe first off-axial optical element 4 a of the imaging optical system 4is extended for ease of understanding. Hereinafter, a reference axislight beam incident on the imaging optical system 4 is referred to as an“incident reference axis light beam”. A reference axis light beam 13exited from the second off-axial optical element 4 b is parallel to orsubstantially parallel to the incident reference axis light beam 12incident on the first off-axial optical element 4 a. An axis 12 a isparallel to the optical path of the incident reference axis light beam12.

Reference numeral 8 denotes a surface normal to the mirror surface R2 ofthe first off-axial optical element 4 a at a point “a” on which theincident reference axis light beam 12 is reflected. Reference numeral 9denotes a surface normal to the mirror surface R4 of the secondoff-axial optical element 4 b at a point “b” on which the reference axislight beam 13 is reflected.

Reference symbol θa denotes an absolute value of an angle formed betweenthe surface normal 8 and the optical path of the incident reference axislight beam 12. Reference symbol θb denotes an absolute value of an angleformed between the surface normal 9 and the axis 12 a parallel to theoptical path of the incident reference axis light beam 12.

In this embodiment, the gravity acts in a lower direction of FIG. 1 andan optical arrangement is made to be relatively less influenced by thegravity. However, the influence of the gravity is not zero, so theoff-axial optical elements are deformed. Further, an optical arrangementin which the original table glass 2 is removed and the carriage 6 andthe members housed therein are tilted in a document feeder may be morelikely to be influenced by the gravity.

In this embodiment, the absolute value θa of the angle formed betweenthe surface normal 8 and the optical path of the incident reference axislight beam 12 and the absolute value θb of the angle formed between thesurface normal 9 and the axis 12 a are set so as to satisfy thefollowing condition.−30°<θa−θb<30°  (1)

The conditional expression (1) is a condition for specifying theabsolute values θa and θb of the angles. When the conditional expression(1) is not satisfied, it is not preferable because the deviation of animaging position due to the deformation of the off-axial optical elementwhich is caused by its own weight becomes larger, making it difficult tocancel the deformation of the surface (mirror surface).

The conditional expression (1) may be more preferably set as follows.−15°<θa−θb<15°  (1a)

In this embodiment, the absolute values θa and θb of the angles are setas follows.θa=11.63°, θb=13.93°Therefore, the following is obtained.θa−θb=−2.3°This value satisfies the conditional expression (1).

In this embodiment, the imaging optical system 4 for image reading doesnot include a refractive surface with power, and the two off-axialoptical elements 4 a and 4 b have the reflective surfaces. This reasonis as follows. When a structure having a refractive function in each ofan incident surface and an exit surface, such as a prism, is used, aproblem resulting from the deformation caused by self weight reduces.However, chromatic aberration is caused by optical properties of a glassmaterial of the prism, so color misregistration occurs in a read image.Therefore, the plurality of off-axial optical elements are used ratherthan an off-axial optical element which is a single block, and each ofthe off-axial optical elements is made of the resin material for ease ofproduction.

Because of a specific feature of the imaging optical system for formingan image on the line sensor, each of the off-axial optical elements hasan outer shape in which a longitudinal (Y-directional) length isdifferent from a lateral (X-directional) length. That is, there are along side and a short side. The longitudinal length can be forcedly madeequal to the lateral length. However, an unnecessary portion of theoff-axial optical element increases accordingly, which increases a sizeof the imaging optical system on the sub-scanning section to be verylarge. When the thickness (Z-direction) of the off-axial optical elementis set to a value smaller than a short-side directional (Y-directional)length, a die structure for producing the off-axial optical element issimplified. Therefore, surface precision is improved, and the size ofthe imaging optical system is reduced.

When the length of the off-axial optical element in the thicknessdirection is set to a shortest length, surface deformation is easilycaused substantially in a mirror surface direction, with the result thata cancel relationship between an arrangement of the off-axial opticalelements whose mirror surfaces are opposed to each other and thedeviation of the imaging position is easily established. On the otherhand, when the off-axial optical element is thickened and thus theshort-side directional length thereof becomes thinnest, the surfacethereof is deformed in a warped shape in the long side direction(X-direction), so the cancel relationship with the arrangement of theoff-axial optical elements whose mirror surfaces are opposed to eachother is not held.

Even when the off-axial optical elements 4 a and 4 b whose mirrorsurfaces R2 and R4 are opposed to each other are not completely opposedto each other, the deviation of the imaging position due to thedeformation of the surfaces thereof can be cancelled. When the sizes ofthe opposed off-axial optical elements are different from each other,the case where they are slightly shifted to each other may be betterthan the case where they are completely opposed to each other.Therefore, in this embodiment, a range (width) of the angle differenceis provided as expressed by the conditional expression (1).

In this embodiment, each of the first and second off-axial opticalelements 4 a and 4 b has a reflective surface with a free surface shape,which is symmetrical with respect to the reference axis La in the mainscanning direction (symmetrical with respect to the YZ-section) andasymmetrical in the sub-scanning direction (within sub-scanningsection).

This is because the imaging optical system 4 in this embodiment is theoff-axial optical system decentered within the sub-scanning section.Therefore, the surface shape within the sub-scanning section isasymmetrical. Although the surface shape within the main scanningsection is symmetrical, both contact ends of each of the off-axialoptical elements in the main scanning direction are connected to a lensbarrel at three points, so one of the contact ends has one point and theother of the contact ends has two points. Therefore, the off-axialoptical element is not completely symmetrical. However, when theoff-axial optical element becomes too asymmetrical, it is difficult tocancel the deviation of the imaging position due to the deformation ofthe surface. Thus, it is preferable that the off-axial optical elementbe symmetrical.

In this embodiment, the thicknesses of the first and second off-axialoptical elements 4 a and 4 b are adjusted based on the outside dimensionof the off-axial optical elements 4 a and 4 b.

This is because, when the sizes of the opposed off-axial opticalelements are different from each other, the amount of deformationchanges. Therefore, the thicknesses of the off-axial optical elementsare adjusted based on the sizes thereof to facilitate the canceling ofdeviation of the imaging position resulting from the deformation.

In this embodiment, when n is a positive integer, the imaging opticalsystem 4 includes 2n (0<n<3) off-axial optical elements.

This is because, when all off-axial optical elements of the imagingoptical system are arranged such that the mirror surfaces thereof areopposed to each other, the deviation of the imaging position can becancelled by all the off-axial optical elements. Therefore, it ispreferable to use the off-axial optical elements which are the multiplesof 2. Note that, when the total number of surfaces is too large, it isdifficult to produce the off axial optical elements. Thus, n is set soas to satisfy 0<n<3 in this embodiment. Although the number of off-axialoptical elements is specified, the number of surfaces in design is notspecified.

In this embodiment, when the first and second off-axial optical elements4 a and 4 b are to be held in a holding portion of the lens barrel,positions of portions of each of the first and second off-axial opticalelements 4 a and 4 b, which are connected to the holding portion of thelens barrel, are adjusted for each thereof.

This reason is to control a deformation shape of the surface, becausethe off-axial optical elements are different from each other in size,shape, and assembly position to the lens barrel.

In this embodiment, when the short-directional length of an arbitraryoff-axial optical element is expressed by Ly and the length thereof inthe thickness direction is expressed by Lz, the following condition issatisfied.1.5<Ly/Lz<20   (2)

The conditional expression (2) is a more detailed conditional expressionfor setting the thickness of the off-axial optical element describedabove to a value smaller than the short-side directional length. WhenLy/Lz is smaller than a lower limit value of the conditional expression(2), it is not preferable because the thickness of the off-axial opticalelement is too large and a time for producing the off-axial opticalelement becomes longer, leading to a problem in which it is difficult tomaintain preferable surface precision. On the other hand, when Ly/Lzexceeds an upper limit value of the conditional expression (2), it isnot preferable because the thickness of the off-axial optical element istoo small and that a sufficient strength cannot be obtained, leading toa problem in which the deformation is caused when assembled to the lensbarrel.

The conditional expression (2) may be more preferably set as follows.1.6<Ly/Lz<15   (2a)

In this embodiment, when the lengths of the first and second off-axialoptical elements 4 a and 4 b in the thickness direction are expressed byLz1 and Lz2 respectively, each of Lz1 and Lz2 is set to 3 mm and amargin between an effective portion and an outer periphery, which is 1mm, is added to a length of an effective light beam area in theshort-side direction at both sides thereof. When the lengths of thefirst and second off-axial optical elements 4 a and 4 b in theshort-side direction are expressed by Ly1 and Ly2, respectively, Ly1 andLy2 are set as follows.Ly1=6.4, Ly2=5.1Therefore, the followings are obtained.Ly1/Lz1=21.3, Ly2/Lz2=1.7Each of the values satisfies the conditional expression (2).

In this embodiment, the aperture stop SP (R3) is provided on an opticalpath between the first and second off-axial optical elements 4 a and 4b, thereby reducing a size of the off-axial reflective surface.

Numerical data in a numerical embodiment of the imaging optical systemfor image reading, which corresponds to Embodiment 1 of the presentinvention as described above, are shown below.

Numerical Embodiment 1

original read width=220 mm

Imaging magnification=−0.189

optical element thickness=3 mm

original side NA=0.016

f_(eg)=29.680 TABLE 1 i Yi Zi θi Ndi Ly 1 0 0 0 1 Object plane (originalsurface) 2 0 166.8934 11.63 1 6.4 Reflective plane 3 −5.1695 154.865823.26 1 Transmission plane (aperture stop) 4 −9.6119 144.5325 13.93 15.1 Reflective plane 5 −7.8571 166.3281 4.60 Imaging plane

Aspheric Configuration

Surface R2

C02=−4.5460E-03 C03=1.8570E-05 C04=−1.9333E-05

C05=1.2781E-06 C06=1.5282E-06 C07=−2.6256E-07

C08=4.0099E-08 C20=−4.7534E-03 C21=6.3040E-05

C22=−4.0753E-06 C23=−5.3171E-08 C24=5.5317E-07

C25=2.3713E-08 C26=−4.2652E-08 C40=2.5124E-06

C41=−6.5956E-08 C42=−2.5347E-09 C43=−8.2587E-10

C44=−8.2235E-10 C60=−3.3116E-09 C61=2.3522E-11

C62=6.4321E-11 C80=3.3081E-12

Surface R4

C02=6.8081E-03 C03=6.1342E-05 C04=−8.7196E-05

C05=−4.3217E-05 C06=1.5179E-05 C07=1.0360E-05

C08=6.6517E-07 C20=6.9865E-03 C21=8.4961E-05

C22=8.3621E-06 C23=5.2533E-07 C24=3.4662E-06

C25=−1.4766E-07 C26=−5.7376E-07 C40=−6.0197E-06

C41=−1.6224E-07 C42=2.0695E-08 C43=7.9461E-10

C44=−6.8943E-09 C60=1.5482E-08 C61=3.6681E-10

C62=−1.4023E-10 C80=−3.0158E-11

As described above, in this embodiment, the imaging optical system 4includes the two off-axial optical elements. Therefore, even when adeformable resin material is used, it is possible to reduce thedeviation of the imaging position due to the deformation caused by theself weight of the off-axial optical element. In addition, it ispossible to obtain the image reading apparatus which is easilymanufactured and has a simple structure.

Embodiment 2

FIG. 3 is a schematic sub-scanning sectional view showing a principalpart of an image reading apparatus to which an imaging optical systemaccording to Embodiment 2 of the present invention is applied. FIG. 4 isa schematic sub-scanning sectional view in the case where the imagingoptical system 34 shown in FIG. 3 is extracted.

A point in this embodiment which is different from Embodiment 1described earlier is that an imaging optical system 34 including first,second, third, and fourth off-axial optical elements 34 a, 34 b, 34 c,and 34 d is applied to an image reading apparatus including a 2:1 mirrorscanning type optical system. Other structures and optical functions areidentical to those in Embodiment 1 and thus the same effect is obtained.

That is, in FIG. 3, a light beam based on image information of anoriginal 37 is imaged on a line sensor 35 serving as a reading means bythe imaging optical system (off-axial optical system) 34 for imagereading.

In this embodiment, the imaging optical system 34 includes the first,second, third, and fourth reflection type off-axial optical elements 34a, 34 b, 34 c, and 34 d which are disposed in order from the original 37side, each of which is made of a resin material. In order to satisfy theconditional expression (1), the first and second off-axial opticalelements 34 a and 34 b are disposed such that the mirror surfaces(off-axial reflective surfaces) R2 and R3 thereof are opposed to eachother and the third and fourth off-axial optical elements 34 c and 34 dare disposed such that the mirror surfaces R5 and R6 thereof are opposedto each other. Each of the first, second, third, and fourth off-axialoptical elements 34 a, 34 b, 34 c, and 34 d is formed such that thelength thereof in the thickness direction (Z-direction) becomes shorterthan the short-side directional (Y-directional) length thereof.

In this embodiment, each of the mirror surfaces (off-axial reflectivesurfaces) of the first, second, third, and fourth off-axial opticalelements 34 a, 34 b, 34 c, and 34 d has a main scanning directional(long-directional) length which is longer than a sub-scanningdirectional (short-directional) length and a main scanning directional(long-directional) thickness which is shorter than a sub-scanningdirectional (short-directional) thickness.

In this embodiment, the original 37 is illuminated with a direct lightbeam emitted from a light source 31 or an indirect light beam emittedtherefrom through a reflection hat 36. A light beam reflected on theoriginal 37 travels through first, second, and third reflecting mirrors33 a, 33 b, and 33 c. Then, an optical path of the light beam is bent inan inner portion of a main body and the light beam is imaged on the linesensor 35 by the imaging optical system 34. At this time, while thefirst, second, and third reflecting mirrors 33 a, 33 b, and 33 c aremoved in the sub-scanning direction, electrical scanning is performed inthe main scanning direction, thereby reading the image information ofthe original 37. The second and third reflecting mirrors 33 b and 33 care moved by half the amount of movement of the first reflecting mirror33 a to make a distance between the original 37 and the line sensor 35constant.

In this embodiment, the image reading apparatus including the 2:1 mirrorscanning type optical system in which a space for moving the lightsource 31 and the first reflecting mirror 33 a is ensured and a portionprotruded downward is reduced is obtained using the above-mentionedimaging optical system 34.

In this embodiment, the optical path of imaging optical system 34 can berelatively freely drawn, so the original 37 surface and the line sensor35 can be relatively freely located. However, there are a package andthe like around a sensor portion of the line sensor 35. In addition, acircuit such as a board and various members for suitably mounting theline sensor 35 are located in rear of the line sensor 35. Therefore, theoriginal 37 surface and the line sensor 35 should be located so as toprevent the optical path from being broken by the line sensor 35 and themembers adjacent thereto. When the line sensor 35 is located under theimaging optical system 34, the various members are protruded downward.In addition to this, mirrors located above the line sensor 35 areinfluenced by heat generated thereby, this causes a deterioration ofimage performance.

In order to avoid such problems, it is preferable that an angle formedbetween an incident reference axis light beam 42 incident on the firstoff-axial optical element 34 a of the imaging optical system 34 and areference axis light beam 44 incident on the line sensor 35 become equalto or smaller than a predetermined angle (45 degrees). In thisembodiment, both the reference axis light beams are parallel to eachother, that is, the angle formed therebetween becomes 0 degrees.

As shown in FIG. 4, the incident reference axis light beam 42 incidenton the first off-axial optical element 34 a of the imaging opticalsystem 34 is extended for the purpose of simplification. A referenceaxis light beam 43 which is exited from the second off-axial opticalelement 34 b or incident on the third off-axial optical element 34 cbecomes parallel to the incident reference axis light beam 42 incidenton the first off-axial optical element 34 a and extended for the purposeof simplification. The reference axis light beam 44 which is exited fromthe fourth off-axial optical element 34 d becomes parallel to theincident reference axis light beam 42 incident on the first off-axialoptical element 34 a.

Reference numeral 38 denotes a surface normal to the mirror surface R2of the first off-axial optical element 34 a at a reflection point “a” onwhich the incident reference axis light beam 42 is reflected. Referencenumeral 39 denotes a surface normal to the mirror surface R3 of thesecond off-axial optical element 34 b at a reflection point “b” on whichthe reference axis light beam 43 is reflected. Reference numeral 40denotes a surface normal to the mirror surface R5 of the third off-axialoptical element 34 c at a reflection point “c” on which the referenceaxis light beam 43 is reflected. Reference numeral 41 denotes a surfacenormal to the mirror surface R6 of the fourth off-axial optical element34 d at a reflection point “d” on which the reference axis light beam 44is reflected.

Reference symbol θa1 denotes an absolute value of an angle formedbetween the surface normal 38 and the optical path of the incidentreference axis light beam 42. Reference symbol θb1 denotes an absolutevalue of an angle formed between the surface normal 39 and the opticalpath of the reference axis light beam 43 (incident reference axis lightbeam 42). Reference symbol θa2 denotes an absolute value of an angleformed between the surface normal 40 and the optical path of thereference axis light beam 43 (incident reference axis light beam 42).Reference symbol θb2 denotes an absolute value of an angle formedbetween the surface normal 41 and the optical path of the reference axislight beam 44 (incident reference axis light beam 42).

In this embodiment, the gravity acts in the downward direction of FIG.4.

In this embodiment, the absolute values θa1, θb1, θa2, and θb2 of therespective angles are set so as to satisfy the conditional expression(1).

That is, in this embodiment, the absolute values θa1 and θb1 of theangles with respect to the first and second off-axial optical elements34 a and 34 b disposed such that the mirror surfaces R2 and R3 thereofare opposed to each other are set as follows.θa1=25°, θb1=25°In addition, the absolute values θa2 and θb2 of the angles with respectto the third and fourth off-axial optical elements 34 c and 34 ddisposed such that the mirror surfaces R5 and R6 thereof are opposed toeach other are set as follows.θa2=20°, θb2=20°Therefore, the followings are obtained.θa1−θb1=0°, θa2−θb2=0°Each of the values satisfies the conditional expression (1).

In this embodiment, when the lengths of the first, second, third, andfourth off-axial optical elements 34 a, 34 b, 34 c, and 34 d in thethickness direction are expressed in order by Lz1, Lz2, Lz3, and Lz4,each of Lz1, Lz2, Lz3, and Lz4 is set to 3 mm and a margin between aneffective portion and an outer periphery, which is 1 mm, is added to alength of an effective light beam area in the short-side direction atboth sides thereof. When the lengths of the first, second, third, andfourth off-axial optical elements 34 a, 34 b, 34 c, and 34 d in theshort-side direction are expressed in order by Ly1, Ly2, Ly3, and Ly4,Ly1, Ly2, Ly3, and Ly4 are set as follows.Ly1=35, Ly2=36Ly3=18, Ly4=26Therefore, the followings are obtained.Ly1/Lz1=11.7, Ly2/Lz2=12.0Ly3/Lz3=6.0, Ly4/Lz4=8.7Each of the values satisfies the conditional expression (2).

In this embodiment, the aperture stop SP (R4) is provided on an opticalpath between the second and third off-axial optical elements 34 b and 34c, thereby reducing a size of the off-axial reflective surface.

Numerical data in Numerical embodiment 2 of the imaging optical systemfor image reading, which corresponds to Embodiment 2 of the presentinvention as described above are shown below.

Numerical Embodiment 2

original read width=304.8

Imaging magnification=−0.22028

Element thickness=3 mm

Original side NA=0.02

f_(eg)=149.45 TABLE 2 i Yi Zi θi Ndi Ly 1 0.0 0.0 0.0 1.0 Object plane(original surface) 2 0.0 454.6167 25.0 1.0 35 Reflective plane 3−30.6418 428.9052 −25.0 1.0 36 Reflective plane 4 −30.6418 463.9052 0.01.0 Transmission plane (aperture stop) 5 −30.6418 498.9052 −20.0 1.0 18Reflective plane 6 −6.2158 469.7955 20.0 1.0 26 Reflective plane 7−6.2158 542.5317 0.0 Imaging plane

Aspheric Configuration

Surface R2

C₀₂=−3.2176e-04 C₀₃=3.7018e-06 C₀₄=−7.5623e-08

C₀₅=−1.8329e-10 C₀₆=−9.3466e-12 C₂₀=1.5416e-03

C₂₁=−4.0469e-07 C₂₂=1.5085e-07 C₂₃=−8.7666e-10

C₂₄=−1.3156e-14 C₄₀=3.4146e-08 C₄₁=1.1840e-12

C₄₂=3.9721e-12 C₆₀=−7.1066e-12

Surface R3

C₀₂=1.8933e-03 C₀₃=−8.4667e-06 C₀₄=−9.6183e-08

C₀₅=4.5947e-11 C₀₆=−2.1682e-11 C₂₀=2.2505e-03

C₂₁=4.9289e-07 C₂₂=1.0880e-07 C₂₃=−1.2602e-09

C₂₄=9.2162e-12 C₄₀=−1.2151e-08 C₄₁=3.2535e-10

C₄₂=2.0246e-12 C₆₀=−7.6249e-12

surface R5

C₀₂=6.9371e-03 C₀₃=−2.0976e-04 C₀₄=2.2162e-06

C₀₅=−2.4220e-08 C₀₆=8.0368e-10 C₂₀=−1.7120e-03

C₂₁=−1.5612e-05 C₂₂=−5.7870e-08 C₂₃=1.7639e-08

C₂₄=−5.390le-10 C₄₀=−9.6716e-08 C₄₁=3.3192e-09

C₄₂=−1.6123e-10 C₆₀=−1.6803e-12

Surface R6

C₀₂=5.3043e-03 C₀₃=−2.9534e-05 C₀₄=−1.7392e-07

C₀₅=−9.4337e-09 C₀₆=−7.7157e-11 C₂₀=−2.0619e-05

C₂₁=−1.3461e-06 C₂₂=−1.7288e-07 C₂₃=−2.3419e-09

C₂₄=−4.0562e-11 C₄₀=−2.2836e-07 C₄₁=2.0954e-09

C₄₂=−5.0235e-11 C₆₀=−1.8984e-11

Embodiment 3

FIG. 5 is a schematic sub-scanning sectional view showing a principalpart of an image reading apparatus to which an imaging optical systemaccording to Embodiment 3 of the present invention is applied. FIG. 6 isa schematic sub-scanning sectional view in the case where the imagingoptical system 54 shown in FIG. 5 is extracted.

A point in this embodiment which is different from Embodiment 1described earlier is that an imaging optical system 54 includes first,second, third, and fourth off-axial optical elements 54 a, 54 b, 54 c,and 54 d. Other structures and optical functions are identical to thosein Embodiment 1 and thus the same effect is obtained.

That is, in FIG. 5, a light beam based on image information of anoriginal 57 is imaged on a line sensor 35 serving as a reading means bythe imaging optical system (off-axial optical system) 54 for imagereading.

In this embodiment, the imaging optical system 54 includes the first,second, third, and fourth reflection type off-axial optical elements 54a, 54 b, 54 c, and 54 d which are disposed in order from the original 7side, each of which is made of a resin material. In order to satisfy theconditional expression (1), the first and fourth off-axial opticalelements 54 a and 54 d are disposed such that the mirror surfaces(off-axial reflective surfaces) R2 and R6 thereof are opposed to eachother and the second and third off-axial optical elements 54 b and 54 care disposed such that the mirror surfaces R3 and R5 thereof are opposedto each other. Each of the first, second, third, and fourth off-axialoptical elements 54 a, 54 b, 54 c, and 54 d is formed such that thelength thereof in the thickness direction becomes shorter than theshort-side directional length thereof.

In this embodiment, the original (object) 7 placed on the original tableglass 2 is illuminated with a light beam emitted from the light source1. A light beam reflected on the original 7 travels through the first,second, and third reflecting mirrors 3 a, 3 b, and 3 c. Then, the lightbeam is imaged on the line sensor 5 by the imaging optical system 54. Atthis time, the original 7 and the carriage 6 are moved relative to eachother in the sub-scanning direction (direction indicated by an arrow A)to two-dimensionally read the original 7.

In order to make the image reading apparatus compact, an optical path ofthe light beam is folded using the first, second, and third reflectingmirrors 3 a, 3 b, and 3 c. The imaging optical system 54 is used to foldthe optical path. The optical path is folded substantially in the formof a combination of two shapes of FIG. 4 by the imaging optical system54 to facilitate the canceling of decentering caused in the opposedoff-axial reflective surfaces. Therefore, preferable imaging performanceis obtained.

In order to obtain more preferable imaging performance, each of theoff-axial reflective surfaces are formed to be a free surface which issymmetrical with respect to the reference axis in the main scanningdirection and asymmetrical with respect to the reference axis in thesub-scanning direction. Therefore, the decentering caused by folding theoptical path in the sub-scanning direction is preferably corrected.

As shown in FIG. 6, an incident reference axis light beam 65 incident onthe first off-axial optical element 54 a is extended for the purpose ofsimplification. A reference axis light beam 66 exited from the secondoff-axial optical element 54 b is extended for the purpose ofsimplification. A reference axis light beam 67 is incident on the thirdoff-axial optical element 54 c. A reference axis light beam 68 is exitedfrom on the fourth off-axial optical element 54 d.

An axis 66 a is parallel to the optical path of the incident referenceaxis light beam 65 at a reflection point “b” of the mirror surface R3 onwhich the reference axis light beam is reflected. An axis 67 a isparallel to the optical path of the incident reference axis light beam65 at a reflection point “c” of the mirror surface R5 on which thereference axis light beam is reflected. An axis 68 a is parallel to theoptical path of the incident reference axis light beam 65 at areflection point “d” of the mirror surface R6 on which the referenceaxis light beam is reflected.

Reference numeral 61 denotes a surface normal to the mirror surface R2of the first off-axial optical element 54 a at a reflection point “a” onwhich the incident reference axis light beam 65 is reflected. Referencenumeral 62 denotes a surface normal to the mirror surface R3 of thesecond off-axial optical element 54 b at a reflection point “b” on whichthe reference axis light beam 66 is reflected. Reference numeral 63denotes a surface normal to the mirror surface R5 of the third off-axialoptical element 54 c at a reflection point “c” on which the referenceaxis light beam 67 is reflected. Reference numeral 64 denotes a surfacenormal to the mirror surface R6 of the fourth off-axial optical element54 d at a reflection point “d” on which the reference axis light beam 68is reflected.

Reference symbol θa1 denotes an absolute value of an angle formedbetween the surface normal 61 and the optical path of the incidentreference axis light beam 65. Reference symbol θa2 denotes an absolutevalue of an angle formed between the surface normal 62 and the axis 66a. Reference symbol θb2 denotes an absolute value of an angle formedbetween the surface normal 63 and the axis 67 a. Reference symbol θb1denotes an absolute value of an angle formed between the surface normal64 and the axis 68 a.

In this embodiment, the gravity acts in the downward direction of FIG.6.

In this embodiment, the absolute values θa1, θb1, θa2, and θb2 of therespective angles are set so as to satisfy the conditional expression(1).

That is, in this embodiment, the absolute values θa1 and θb1 of theangles with respect to the first and fourth off-axial optical elements54 a and 54 d disposed such that the mirror surfaces R2 and R6 thereofare opposed to each other are set as follows.θa1=18.5°, θb1=22.425°In addition, the absolute values θa2 and θb2 of the angles with respectto the second and third off-axial optical elements 54 b and 54 cdisposed such that the mirror surfaces R3 and R5 thereof are opposed toeach other are set as follows.θa2=61.411°, θb2=62.837°Therefore, the followings are obtained.θa1−θb1=−3.92°, θa2−θb2=−1.426°Each of the values satisfies the conditional expression (1).

In this embodiment, when the lengths of the first and fourth off-axialoptical elements 54 a and 54 d in the thickness direction are expressedby Lz1 and Lz4, each of Lz1 and Lz4 is set to 6 mm. When the length ofthe second off-axial optical element 54 b in the thickness direction isexpressed by Lz2, Lz2 is set to 5 mm. When the length of the thirdoff-axial optical element 54 c in the thickness direction is expressedby Lz3, Lz3 is set to 4 mm. A margin between an effective portion and anouter periphery, which is 1 mm, is added to a length of an effectivelight beam area in the short-side direction at both sides thereof. Whenthe lengths of the first, second, third, and fourth off-axial opticalelements 54 a, 54 b, 54 c, and 54 d in the short-side direction areexpressed in order by Ly1, Ly2, Ly3, and Ly4, Ly1, Ly2, Ly3, and Ly4 areset as follows.Ly1=14, Ly2=12Ly3=9, Ly4=11Therefore, the followings are obtained.Ly1/Lz1=2.3, Ly2/Lz2=2.4Ly3/Lz3=2.25, Ly4/Lz4=1.8Each of the values satisfies the conditional expression (2).

In this embodiment, the aperture stop SP (R4) is provided on an opticalpath between the second and third off-axial optical elements 54 b and 54c, thereby reducing a size of the off-axial reflective surface.

Numerical data in Numerical embodiment 3 of the imaging optical systemfor image reading, which corresponds to Embodiment 3 of the presentinvention as described above are shown below.

Numerical Embodiment 3

Original read width=304.8

Imaging magnification=−0.22028

Element thickness: Lz1=6, Lz2=5, Lz3=4, Lz4=6

Original side NA=0.02

f_(eq)=49.912 TABLE 3 i Yi Zi θi Ndi Ly 1 0.0 0.0 0.0 1.0 Object plane(original surface) 2 0.0 176.6883 18.5 1.0 14 Reflective plane 3 −8.2419165.7509 61.4113 1.0 12 Reflective plane 4 8.2154 166.9530 85.8225 1.0Transmission plane (aperture stop) 5 24.1746 168.1186 62.8366 1.0 9Reflective plane 6 14.9929 157.1182 22.4254 1.0 11 Reflective plane 717.5197 186.0000 5.0 Imaging planeSurface R2

C02=−1.3207E-03 C03=2.6667E-06 C04=3.3489E-06

C05=5.3173E-06 C06=−1.3333E-08 C07=−2.6007E-09

C08=−2.5014E-10 C20=−1.1446E-03 C21=−5.7000E-05

C22=1.6118E-06 C23=−7.1879E-08 C24=2.1492E-09

C25=1.2028E-10 C26=5.8979E-11 C40=−1.0980E-07

C41=2.3051E-08 C42=−9.6151E-10 C43=4.6901E-11

C44=−6.7039E-12 C60=4.8532E-11 C61=−8.2096E-12

C62=5.1746E-13 C80=−2.4227E-15

Surface R3

C02=2.3797E-03 C03=−2.8576E-06 C04=3.6486E-06

C05=9.9884E-08 C06=−2.0000E-08 C07=−3.5678E-09

C08=−1.8740E-10 C20=1.2266E-03 C21=−7.3777E-05

C22=−1.6000E-07 C23=−2.6667E-08 C24=2.1607E-09

C25=−2.0065E-10 C26=1.0043E-10 C40=−8.0582E-07

C41=4.0054E-08 C42=2.0023E-09 C43=1.2699E-10

C44=−1.2974E-11 C60 =7.7270E-10 C61=−2.5130E-11

C62=−1.5557E-12 C80=−3.8483E-13

Surface R5

C02=5.4062E-03 C03=5.3333E-06 C04=3.8756E-06

C05=6.9415E-07 C06=2.0000E-07 C07=−5.4455E-08

C08=−6.0202E-09 C20=−2.6134E-03 C21=−1.6073E-05

C22=−6.1166E-06 C23=−3.3333E-07 C24=6.0000E-09

C25=−9.2388E-09 C26=−1.4212E-09 C40=−1.5265E-06

C41=−1.4026E-07 C42=3.1323E-09 C43=−1.4899E-10

C44=−1.9827E-12 C60=1.5752E-09 C61=4.9067E-11

C62=−4.1013E-12 C80=−9.2414E-13

Surface R6

C02=1.0000E-02 C03=−1.1951E-05 C04=8.0000E-07

C05=1.2553E-07 C06=1.4258E-07 C07=−1.2965E-08

C08=−9.3779E-10 C20=4.8806E-03 C21=−1.3709E-05

C22=−2.0841E-06 C23=−2.7268E-07 C24=−1.4302E-08

C25=2.0567E-09 C26=−1.3279E-10 C40=−1.3224E-06

C41=−8.6942E-08 C42=−7.0696E-09 C43=−4.4229E-10

C44=2.6856E-11 C60=−4.1850E-10 C61=−6.8174E-11

C62=−5.1278E-12 C80=1.2409E-13

This application claims priority from Japanese Patent Application No.2005-029298 filed on Feb. 4, 2005, which is hereby incorporated byreference herein.

1-8. (canceled)
 9. An imaging optical system for image reading, in whichimage information on a surface of an original is imaged on a line sensorand the image information is read by the line sensor, comprising: afirst off-axial optical element, a second off-axial optical element, athird off-axial optical element and a fourth off-axial optical elementdisposed in order from an original side, wherein each of the first,second, third and fourth off-axial optical elements is a reflection-typeoff-axial optical element having free-form surface shape and is made ofa resin material, wherein a main scanning direction is a line directionof the line sensor and a sub-scanning direction is a directionorthogonal to the main scanning direction, a length of each of thefirst, second, third and fourth off-axial optical elements in the mainscanning direction is longer than a length thereof in the sub-scanningdirection and a thickness thereof is smaller than the length thereof inthe sub-scanning direction, wherein in a sub-scanning section in whichthe main scanning direction corresponds to a normal, the followingcondition is satisfied,−30°<θa1−θb1<30°, where θa1 represents an absolute value of a firstangle formed between a surface normal to a reflective surface of thefirst off-axial optical element at a reflection point of the reflectivesurface of the first off-axial optical element at which a reference axislight beam is reflected and a reference axis light beam incident on thereflective surface of the first off-axial optical element and θb1represents an absolute value of a second angle formed between a surfacenormal to a reflective surface of the second off-axial optical elementat a reflection point of the reflective surface of the second off-axialoptical element at which the reference axis light beam is reflected andthe reference axis light beam incident on the reflective surface of thefirst off-axial optical element, and wherein in the sub-scanningsection, the following condition is satisfied,−30°<θa2−θb2<30°, where θa2 represents an absolute value of a thirdangle formed between a surface normal to a reflective surface of thethird off-axial optical element at a reflection point of the reflectivesurface of the third off-axial optical element at which a reference axislight beam is reflected and the reference axis light beam incident onthe reflective surface of the first off-axial optical element and θb2represents an absolute value of a fourth angle formed between a surfacenormal to a reflective surface of the fourth off-axial optical elementat a reflection point of the reflective surface of the fourth off-axialoptical element on which the reference axis light beam is reflected andthe reference axis light beam incident on the reflective surface of thefirst off-axial optical element.
 10. An imaging optical system for imagereading according to claim 15, wherein each of said off-axial opticalelements comprises a reflective surface which is symmetrical withrespect to a reference axis of the imaging optical system in the mainscanning direction and asymmetrical with respect to the reference axisin the sub-scanning direction.
 11. An imaging optical system for imagereading according to claim 16, wherein said plurality of off-axialoptical elements include thicknesses different from one another.
 12. Animaging optical system for image reading according to claim 15, whereinsaid plurality of off-axial optical elements are held in a holdingportion of a lens barrel and the off-axial optical elements aredifferent from one another in a position of a portion of the off-axialoptical element which abuts the holding portion of the lens barrel. 13.An imaging optical system for image reading according to claim 15,wherein the following condition is satisfied,1.5<Ly/Lz<20, where Lz represents a thickness of an arbitrary off-axialoptical element of the first, second, third and fourth off-axial opticalelements and Ly represents a length thereof of in the sub-scanningdirection.
 14. An image reading apparatus, comprising: the imagingoptical system for image reading according to claim 15; an originaltable on which said original is placed; and said line sensor.